Crack initiation patterns at electrode edges in multilayer ferroelectric actuators

In multilayer ferroelectric actuators, electrode edges are the main source of fracture due to the generation of non-uniform electric fields in their vicinity. The electric fields, in turn, induce incompatible strain fields and hence concentrated stresses, which may cause the ceramic to crack. In this paper, the crack initiation from the electrode edges is simulated using a phase-field model. This model is based on variational formulations of brittle crack propagation and domain evolution in ferroelectric materials. The simulation results show different crack initiation patterns depending on the bonding conditions between the ceramic and electrode layers. Three extreme conditions are considered, which are the fully cofired, partially cofired, and separated layers. The crack initiation patterns can be either delimitation along the electrode-ceramic interface or oblique cracking from the electrode into the material. The calculations suggest a mechanism explaining the experimentally observed crack branches near the electrode edges. The effects of the ceramic layer thickness and length of the internal electrode on the crack initiation are also evaluated. Crack initiation patterns at electrode edges in multilayer ferroelectric actuators 2